A statistical model to transform election poll proportions into - PowerPoint PPT Presentation

A statistical model to transform election poll proportions into representatives: The Spanish case Jose M. Pavia Elections and Public Opinion Research Group Universitat de Valencia 13-15 September 2013, Lancaster University

Introduction Opinion and election polls are ordinarily used in western democracies as a tool to know and understand public desires and to assess policies and governments. Polls are usually designed to forecast share of votes, although election results are mediated for the particular electoral formula each system uses. Jose M. Pavia 2 Translating proportions into seats. The Spanish case.

Introduction Different proposals have been suggested to bridge the gap between estimates proportions and election outcomes, such as the so-called cube law that emerges in unimodal plurality systems (e.g., Gudgin and Taylor, 2012) . This work tries to offer some answers to the issue of translating votes into seats in the context of the Spanish elections. Gudgin and Taylor, 2012, Seats, votes, and the spatial organisation of elections , ECPR Press. Jose M. Pavia 3 Translating proportions into seats. The Spanish case.

The Spanish (Congress) Election System • The Spanish Parliament has 350 seats. • Spain is divided into 52 constituencies (50 provinces plus the cities of Ceuta and Melilla) . • Ceuta as well as Melilla elect a seat each. • At least 2 seats are elected in each province. • The Hamilton rule is used to apportion the remaining 248 seats among the provinces, using province total populations as weights. • Votes are casted to party closed lists. Jose M. Pavia 4 Translating proportions into seats. The Spanish case.

The Spanish (Congress) Election System • Within each constituency, seats are allocated to parties using the d’Hondt rule. • To opt to representation in a constituency, a party needs to reach at least 3% of the valid votes of the constituency. • There are three national parties (PP, PS and IU) and a fourth (UPyD) emerging. • There are several strong regional parties. CiU and ERC in Catalonia and PNV and HB-Amaiur in The Basque Country. BNG and CC and sometimes PAR-CHA, PA,… also used to reach representation. Jose M. Pavia 5 Translating proportions into seats. The Spanish case.

The Spanish (Congress) Election System According to many commentators (e.g., Rae and Ramírez, 1993; Urdanoz, 2008; Santayola Machetti, 2011) , the Spanish system, being nominally a proportional system, de facto favours big parties as a consequence of the cumulative effect that small constituencies and the d’Hondt rule have on breaking proportionality. Rae and Ramírez. 1993. El Sistema Electoral Español: Quince Años de Experiencia , McGraw-Hill. Urdanoz, 2008, “El maquiavélico sistema electoral español” El País , 16 February, 35. Santoyola, 2011. “III Jornadas de derecho parlamentario. La reforma de la ley orgánica del régimen electoral general”, Cuadernos Manuel Giménez Abab , 1, 95-98. Jose M. Pavia 6 Translating proportions into seats. The Spanish case.

Spanish Constituencies 1-3 seats: 11 districts 4-6 seats: 24 districts 7-8 seats: 10 districts 10-16 seats: 5 districts +30 seats: 2 districts 7

The d’Hondt rule The d’Hondt law is a particular case of a divisor rule that attempts to make the averages between votes received and seats gained similar among parties. Given K parties obtaining p 1 , p 2 , …, p K proportion of votes and M seats to allocate, the d’Hondt rule proceeds as follows: (1) Calculate the K × M matrix of quotients p k /d j , k =1,…,K, j =1,..., M , with d j = j . (2) Select the M largest quotients and give the corresponding parties a seat for each of their largest quotients . Jose M. Pavia 8 Translating proportions into seats. The Spanish case.

The d’Hondt rule Depending on the sequence of denominators d j chosen different rules emerge, such as the first-past-the-poll and the winner- take-all rules (d j =1) or the Sainte-Lagüe (d j =2j-1) and the modified Sainte-Lagüe rules. Example : 7 seats distributed among four parties (A, B, C, and D) receiving 45%, 32%, 15%, and 8% of votes produces 4, 2, 1, and 0 seats. Seats Party 1 2 3 4 5 6 7 45.0 1 22.5 3 15.0 5 11.3 7 A 9.0 7.5 6.4 32.0 2 16.0 4 10.7 B 8.0 6.4 5.3 4.6 14.0 6 C 7.5 4.7 3.5 2.8 2.3 2.0 D 8.0 4.0 2.7 2.0 1.6 1.3 1.1 Jose M. Pavia 9 Translating proportions into seats. The Spanish case.

Can election poll district proportions be used directly to generate seats forecasts? • In election polls, at most a couple of thousand electors are typically interviewed. (Average 2008-2011: 1,480. Last week 2011 election: 4,726) • Predictions of share of votes are only reliable in (national or regional) aggregated terms. • But representatives are elected in subnational constituencies: provinces. Jose M. Pavia 10 Translating proportions into seats. The Spanish case.

Proportion estimates in districts show extreme variability Constituency of Toledo. A de facto two party district, 6 seats in 2011 Election. National sample size: 2500. Sampling in ideal conditions. Normal approximation. 2011 General Election. Two party share of votes, PP: 68.22%; PS: 33.78%. Jose M. Pavia 11 Translating proportions into seats. The Spanish case.

… and seat allocation produces aggregate bias Although when there are many constituencies we might expect the district biases to cancel one another out and that the prediction for the whole Parliament would have no bias, data from real elections in Spain show that it is not usually the case ( Delicado and Udina, 2001; Udina and Delicado, 2005 ). According to those authors, this may occur because (i) some locally important parties contend only in a few districts and due to (ii) several districts may have a similar bias as a consequence of general voting national patterns and small constituency sizes. Delicado and Udina, 2001, “¿Cómo y cuánto fallan los sondeos electorales?” Revista Española de Investigaciones Sociológicas, 96, 123-150. Udina and Delicado, 2005, “Estimating parliamentary composition through electoral polls” Journal of the Royal Statistical Society-A, 168, 387-399. Jose M. Pavia 12 Translating proportions into seats. The Spanish case.

Poll Variability & Bias: Parliament Forecasts CV(PP)=3% Bias(PP)=-1.5 Bias(PS)= 0.3 CV(PS)=5% Bias(IU)= 1.7 CV(IU)=19% The points in the scatterplot represent 2000 Parliaments projected on the plane defined for the two main principal components obtained from 2000 simulated polls of size 2500 using the 2011 Spanish General election final results. The two-components captured variance is 44.6%. The arrows, starting from the average point of forecasted Parliaments, represent the directions favouring the three main parties. The blue square marks the position of the real Parliament and shows visually that there is a significant bias in the estimation of Parliamentary composition. 13

Poll Proportions: Less Variability & No Bias CV(PP) = 2.5% CV(PS) = 4.0% CV(IU) = 9.0% The points in the scatterplot represent 2000 proportion polls projected on the plane defined for the two main principal components obtained from 2000 simulated polls of size 2500 using the 2011 Spanish General election final results. The two-components captured variance is 42.7%. The arrows, starting from the average point, represent the directions favouring the three main parties. The blue square marks the position of the proportions and shows visually that there is no bias in the estimation of proportions. 14

Looking for historical relationships between votes and seats (1977-2011) y = -.97 + 1.18x R 2 = 0.98 Jose M. Pavia 15 Translating proportions into seats. The Spanish case.

Modelling the votes-seats relationship A strong linear relationship exists between the proportions of votes and seats a party gains. Despite the strong global relationship (R 2 =0.98), it seems that a single equation for each party can yield better results. For small national parties, the linear relationship seems to work after 4% of votes, a logit transformation maybe could be useful for the whole range. For small regional and for sporadic parties, as well as the possible existence of selection bias (only parties reaching Parliament are displayed in the figure ), an ordinal logit model with additional covariates could be more adequate. Jose M. Pavia 16 Translating proportions into seats. The Spanish case.

Model-I 1. Fit univariate linear equations for PP and PS. 2. Fit a univariate linear equation for small national parties (range 4%-12% of national votes). 3. Fit a univariate linear equation for Catalonian regional parties. 4. Fit a univariate linear equation for regional parties from The Basque Country. 5. Fit a univariate linear equation for other regional parties. 6. Round to the nearest integer the seats forecasts (except for point 5 predictions that are round to zero). 7. And, given that the Spanish system favours the party obtaining the great support, to assign to the biggest party the difference to 350 seats. Jose M. Pavia 17 Translating proportions into seats. The Spanish case.